A tower is 50 meters high. Its shadow is x meters shorter when the sun’s altitude is 45° than when it is 30°. The value of x in metres is
50(√3 - 1)
Let the height of the tower be h = 50 meters.
When the sun's altitude is 30°, the shadow length is \(l_1 = \frac{h}{\tan 30^\circ} = \frac{50}{\frac{1}{\sqrt{3}}} = 50\sqrt{3}\) meters.
When the sun's altitude is 45°, the shadow length is \(l_2 = \frac{h}{\tan 45^\circ} = \frac{50}{1} = 50\) meters.
The difference in shadow lengths is \(x = l_1 - l_2 = 50\sqrt{3} - 50 = 50(\sqrt{3} - 1)\) meters.
Therefore, the value of x is 50(√3 - 1) meters.
Similar Questions
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
Which one of the following combinations of measurements can form the sides of a triangle?
If \( \frac{3}{(x+2)(x+1)} = \frac{a}{2x+1} + \frac{b}{x^2+1} \) be an identity, then the value of \( b \) is:
From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is \( \sqrt{3} = 1.732 \):
The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 PM will be
If Sin 31° = x/y, the value of Sec 31° - Sin 59° is
The value of (sec245° - cot245°) - (sin230° + sin260°) is
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
Important Questions from Trigonometry
(secθ + tanθ)/(secθ - tanθ) is equal to:
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
The value of sin θ and cos θ when the angle θ is 0 ≤ θ ≤ 90°, is ______
